xy>1且log3(x)log3(y)=9求xy最小值

问题描述:

xy>1且log3(x)log3(y)=9求xy最小值
如题

∵log3(x)+log3(y)≥2√log3(x)log3(y) 且log3(x)log3(y)=9
∴log3(x)+log3(y)≥6
∵log3(x)+log3(y)=log3(xy)≥6且xy>1
∴log3(x)+log3(y)=log3(xy)≥log3(216)
∴xy最小值为216